We will need to consider a parametric generalization of the framework of the previous section; cf. [1]}, [2]}. Suppose that \(\)  is a smooth manifold and \(\mathbf {Y}: \rightarrow _*\)  a smooth function.
We denote
\( \mathcal {M}_\Gamma (J_\mathbf {Y}) := \coprod _{s \in } \mathcal {M}_\Gamma (J_{\mathbf {Y}(s)}).\) 
